Simulating chi-square data through algorithms in the presence of uncertainty

Muhammad Aslam; Osama H. Arif; Muhammad Aslam; Osama H. Arif

doi:10.3934/math.2024588

AIMS Mathematics

2024, Volume 9, Issue 5: 12043-12056. doi: 10.3934/math.2024588

Previous Article Next Article

Research article

Simulating chi-square data through algorithms in the presence of uncertainty

Muhammad Aslam ^,,
Osama H. Arif

Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia

Received: 11 February 2024 Revised: 15 March 2024 Accepted: 20 March 2024 Published: 27 March 2024
MSC : 62A86

This paper presents a novel methodology aimed at generating chi-square variates within the framework of neutrosophic statistics. It introduces algorithms designed for the generation of neutrosophic random chi-square variates and illustrates the distribution of these variates across a spectrum of indeterminacy levels. The investigation delves into the influence of indeterminacy on random numbers, revealing a significant impact across various degrees of freedom. Notably, the analysis of random variate tables demonstrates a consistent decrease in neutrosophic random variates as the degree of indeterminacy escalates across all degrees of freedom values. These findings underscore the pronounced effect of uncertainty on chi-square data generation. The proposed algorithm offers a valuable tool for generating data under conditions of uncertainty, particularly in scenarios where capturing real data proves challenging. Furthermore, the data generated through this approach holds utility in goodness-of-fit tests and assessments of variance homogeneity.
- chi-square distribution,
- random numbers,
- simulation,
- classical statistics,
- neutrosophic statistics
Citation: Muhammad Aslam, Osama H. Arif. Simulating chi-square data through algorithms in the presence of uncertainty[J]. AIMS Mathematics, 2024, 9(5): 12043-12056. doi: 10.3934/math.2024588

Related Papers:

Abstract

This paper presents a novel methodology aimed at generating chi-square variates within the framework of neutrosophic statistics. It introduces algorithms designed for the generation of neutrosophic random chi-square variates and illustrates the distribution of these variates across a spectrum of indeterminacy levels. The investigation delves into the influence of indeterminacy on random numbers, revealing a significant impact across various degrees of freedom. Notably, the analysis of random variate tables demonstrates a consistent decrease in neutrosophic random variates as the degree of indeterminacy escalates across all degrees of freedom values. These findings underscore the pronounced effect of uncertainty on chi-square data generation. The proposed algorithm offers a valuable tool for generating data under conditions of uncertainty, particularly in scenarios where capturing real data proves challenging. Furthermore, the data generated through this approach holds utility in goodness-of-fit tests and assessments of variance homogeneity.

References

[1]	P. Schober, T. R. Vetter, Chi-square tests in medical research, Anesth. Analg., 129 (2019), 1193. https://doi.org/10.1213/ANE.0000000000004410 doi: 10.1213/ANE.0000000000004410
[2]	M. V. Koutras, S. Bersimis, D. L. Antzoulakos, Improving the performance of the chi-square control chart via runs rules, Methodol. Comput. Appl. Probab., 8 (2006), 409–426. https://doi.org/10.1007/s11009-006-9754-z doi: 10.1007/s11009-006-9754-z
[3]	N. T. Thomopoulos, Essentials of Monte Carlo simulation: Statistical methods for building simulation models, New York: Springer, 2013. https://doi.org/10.1007/978-1-4614-6022-0
[4]	M. A. Jdid, R. Alhabib, A. A. Salama, Fundamentals of neutrosophical simulation for generating random numbers associated with uniform probability distribution, Neutrosophic Sets Sy., 49 (2022), 92–102. https://doi.org/10.5281/zenodo.6426375 doi: 10.5281/zenodo.6426375
[5]	M. A. Jdid, R. Alhabib, A. A. Salama, The static model of inventory management without a deficit with Neutrosophic logic, International Journal of Neutrosophic Science, 16 (2021), 42–48. https://doi.org/10.54216/IJNS.160104 doi: 10.54216/IJNS.160104
[6]	J. F. Monahan, An algorithm for generating chi random variables, ACM T. Math. Software, 13 (1987), 168–172. https://doi.org/10.1145/328512.328522 doi: 10.1145/328512.328522
[7]	E. Shmerling, Algorithms for generating random variables with a rational probability-generating function, Int. J. Comput. Math., 92 (2015), 2001–2010. https://doi.org/10.1080/00207160.2014.945918 doi: 10.1080/00207160.2014.945918
[8]	N. Ortigosa, M. Orellana-Panchame, J. C. Castro-Palacio, P. F. de Córdoba, J. M. Isidro, Monte Carlo simulation of a modified Chi distribution considering asymmetry in the generating functions: Application to the study of health-related variables, Symmetry, 13 (2021), 924. https://doi.org/10.3390/sym13060924 doi: 10.3390/sym13060924
[9]	L. Devroye, A simple algorithm for generating random variates with a log-concave density, Computing, 33 (1984), 247–257. https://doi.org/10.1007/BF02242271 doi: 10.1007/BF02242271
[10]	L. Devroye, Nonuniform random variate generation, Handbooks in Operations Research and Management Science, 13 (2006), 83–121. https://doi.org/10.1016/S0927-0507(06)13004-2 doi: 10.1016/S0927-0507(06)13004-2
[11]	L. Devroye, Random variate generation for the generalized inverse Gaussian distribution, Stat. Comput., 24 (2014), 239–246. https://doi.org/10.1007/s11222-012-9367-z doi: 10.1007/s11222-012-9367-z
[12]	E. A. Luengo, Gamma Pseudo random number generators, ACM Comput. Surv., 55 (2022), 1–33. https://doi.org/10.1145/3527157 doi: 10.1145/3527157
[13]	H. Yao, T. Taimre, Estimating tail probabilities of random sums of phase-type scale mixture random variables, Algorithms, 15 (2022), 350. https://doi.org/10.3390/a15100350 doi: 10.3390/a15100350
[14]	T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein, Introduction to algorithms, Massachusetts: MIT Press, 2022.
[15]	D. H. Pereira, Itamaracá: A novel simple way to generate Pseudo-random numbers, Cambridge Open Engage, 2022. https://doi.org/10.33774/coe-2022-zsw6t doi: 10.33774/coe-2022-zsw6t
[16]	F. Smarandache, Introduction to neutrosophic statistics, Craiova: Romania-Educational Publisher, 2014.
[17]	F. Smarandache, Neutrosophic statistics is an extension of interval statistics, while Plithogenic Statistics is the most general form of statistics (second version), International Journal of Neutrosophic Science, 19 (2022), 148–165. https://doi.org/10.54216/ IJNS.190111 doi: 10.54216/IJNS.190111
[18]	J. Q. Chen, J. Ye, S. G. Du, Scale effect and anisotropy analyzed for neutrosophic numbers of rock joint roughness coefficient based on neutrosophic statistics, Symmetry, 9 (2017), 208. https://doi.org/10.3390/sym9100208 doi: 10.3390/sym9100208
[19]	J. Chen, J. Ye, S. G. Du, R. Yong, Expressions of rock joint roughness coefficient using neutrosophic interval statistical numbers, Symmetry, 9 (2017), 123. https://doi.org/10.3390/sym9070123 doi: 10.3390/sym9070123
[20]	M. Aslam, Truncated variable algorithm using DUS-neutrosophic Weibull distribution, Complex Intell. Syst., 9 (2023), 3107–3114.
[21]	F. Smarandache, Neutrosophic statistics is an extension of interval statistics, while Plithogenic statistics is the most general form of statistics, Neutrosophic Computing and Machine Learning, 23 (2022), 21–38.
[22]	R. Alhabib, M. M. Ranna, H. Farah, A. A. Salama, Some neutrosophic probability distributions, Neutrosophic Sets Sy., 22 (2018), 30–38.
[23]	Z. Khan, A. Al-Bossly, M. M. A. Almazah, F. S. Alduais, On statistical development of neutrosophic gamma distribution with applications to complex data analysis, Complexity, 2021 (2021), 3701236. https://doi.org/10.1155/2021/3701236 doi: 10.1155/2021/3701236
[24]	R. A. K. Sherwani, M. Aslam, M. A. Raza, M. Farooq, M. Abid, M. Tahir, Neutrosophic normal probability distribution–A spine of parametric neutrosophic statistical tests: properties and applications, In: Neutrosophic operational research, Cham: Springer, 2021,153–169. https://doi.org/10.1007/978-3-030-57197-9_8
[25]	C. Granados, Some discrete neutrosophic distributions with neutrosophic parameters based on neutrosophic random variables, Hacet. J. Math. Stat., 51 (2022), 1442–1457. https://doi.org/10.15672/hujms.1099081 doi: 10.15672/hujms.1099081
[26]	C. Granados, A. K. Das, B. Das, Some continuous neutrosophic distributions with neutrosophic parameters based on neutrosophic random variables, Advances in the Theory of Nonlinear Analysis and its Application, 6 (2023), 380–389.
[27]	Y. H. Guo, A. Sengur, NCM: Neutrosophic c-means clustering algorithm, Pattern Recogn., 48 (2015), 2710–2724. https://doi.org/10.1016/j.patcog.2015.02.018 doi: 10.1016/j.patcog.2015.02.018
[28]	H. Garg, Nancy, Algorithms for single-valued neutrosophic decision making based on TOPSIS and clustering methods with new distance measure, AIMS Mathematics, 5 (2020), 2671–2693. https://doi.org/10.3934/math.2020173 doi: 10.3934/math.2020173
[29]	M. Aslam, Simulating imprecise data: sine-cosine and convolution methods with neutrosophic normal distribution, J. Big Data, 10 (2023), 143. https://doi.org/10.1186/s40537-023-00822-4 doi: 10.1186/s40537-023-00822-4
[30]	M. Aslam, Uncertainty-driven generation of neutrosophic random variates from the Weibull distribution, J. Big Data, 10 (2023), 177. https://doi.org/10.1186/s40537-023-00860-y doi: 10.1186/s40537-023-00860-y
[31]	M. Aslam, F. S. Alamri, Algorithm for generating neutrosophic data using accept-reject method, J. Big Data, 10 (2023), 175. https://doi.org/10.1186/s40537-023-00855-9 doi: 10.1186/s40537-023-00855-9
[32]	M. Catelani, A. Zanobini, L. Ciani, Uncertainty interval evaluation using the Chi-square and Fisher distributions in the measurement process, Metrol. Meas. Syst., 17 (2010), 195–204. https://doi.org/10.2478/v10178-010-0017-5 doi: 10.2478/v10178-010-0017-5
[33]	R. H. Hariri, E. M. Fredericks, K. M. Bowers, Uncertainty in big data analytics: survey, opportunities, and challenges, J. Big Data, 6 (2019), 44. https://doi.org/10.1186/s40537-019-0206-3 doi: 10.1186/s40537-019-0206-3

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)